The term "promo box" is used generically to describe custom made boxes that are used to store Japanese mini LPs.
The majority of these boxes are created by a Japanese company "Disk Union" and they are truly promotional. They are "given away" as an incentive to people who purchase the entire set of a particular release. Each release is usually for one artist and also is usually on or around a specific date.
For example, Toshiba may release 10 mini LPs for a single artist over a period of a month or so (if not all on the same day). Disk Union purchase a set number of these and hold them in stock until the last is released. Meanwhile Disk Union create a special box using artwork usually based on, or directly derived from, one of the artist's releases.
Disk Union offer the box as an incentive to those who purchase all 10 titles in one lot from Disk Union.
These releases from Disk Union are often also accompanied by "promo obis" and, more rarely a replica of another 33rpm or 45rpm cover (such as Zappa's Uncle Meat Box)..
Occasionally the record companies produce boxes for housing sets. In most cases these are sold at a markup (therefore they cannot be considered strictly "promotional"). Often the CDs contained within the box cannot be purchased separately (other than on ebay of course). The Rolling Stones "Bigger Bang 2006" box is a good example.
Home made one offs
These are "labours of love" and usually are not sold. There are exceptions but anyone selling these usually makes it pretty clear. Also, the quality ranges significantly.
In recent years a number of highly popular boxes have been illegally manufactured and sold on eBay and elsewhere (Amazon second hand dealers). These included the black Led Zeppelin Box and both Mono and Stereo Beatles Remasters. Thousands have been made and, arguably, there are as many fakes as there are originals.
There are also some unofficial releases (not Disk Union and not Manufacturer releases - fakes in effect). An example is the "Exciting the Who" box (the 2005 release, not the 2006 version which is official).
Are these legal?
The official releases are obviously legal.
The Disk Union boxes are also legit. There are occasions when Disk Union has announced a box and then has not produced it. It is believed that this happens because they have not been able to finalise the usage of the artwork (any artwork) on the box (Pete Townshend for example).
The others are (theoretically) illegal and would normally also contain fake mini-lps, but not necessarily. If the collector has filled the box from a number of different sources then the box will likely contain a mix of genuine and fake mini LPs.
Buying these boxes
Disk Union does not ship these boxes outside Japan. The only way to buy them is from someone in Japan or on eBay.